Prerequisites

The calculations were made in R using R-Studio. The structure of the code is essentially based on the structure of the text. The raw code is in the file order_of_code.R. The file extended with Markdown is order_of_code-doc.RMD and the file order_of_code-doc.html is generated from it.

Note: The base path for rmd files is the folder in which they are located, not the r-project. Consequently, order_of_code.R and order_of_code-doc.RMD are both located in the root folder of the project.

Depending on the hardware, the subsequent code can run for several hours or even a few days.

Install “Just Another Gibbs Sampler” (JAGS) (Plummer 2003) if you want to run the Bayesian analyses anew. Version 4.3 - as used here - can be downloaded in pre-compiled form for a number of OS here: https://sourceforge.net/projects/mcmc-jags/ . The manual can be found here: https://people.stat.sc.edu/hansont/stat740/jags_user_manual.pdf

The code makes extensive use of the function source to call external code. Thus, the main part of the code remains slim, well structured and readable.

Install required packages, set some options and link the sources for the helper functions.

Remark: Depending on your R version the package osmplotr may be installed from github using devtools::install_github ("ropensci/osmplotr").

require(pacman) || install.packages("pacman")
## Loading required package: pacman
## [1] TRUE
pacman::p_load(coda, cowplot, demogR, dplyr, flexsurv, ggplot2, ggrepel, grid, 
               gridExtra, HMDHFDplus, kableExtra, Metrics, mortAAR, osmdata, 
               psych, readxl, reshape2, rjags, runjags, sf, tidyr, ggspatial)

options(scipen = 999)
options(dplyr.summarise.inform = FALSE)

source("./functions/bayes_cat_poisson.R")
source("./functions/gomp_MLE.R")
source("./functions/gomp_MLE_adapted.R")
source("./functions/gomp_MLE_interval.R")
source("./functions/gomp_anthr_age.R")
source("./functions/gomp_anthr_age_r.R")
source("./functions/gomp_known_age.R")
source("./functions/gomp_known_age_r.R")
source("./functions/helper_functions.R")
source("./functions/lt_MC.R")
source("./functions/lt_MC_Gomp.R")
RNGkind("L'Ecuyer-CMRG") # conservative random number generator to avoid periodicity

Important for saving time: Decide to run extensive code anew (app. 6 h +). In addition, you can set the folder for preprocessed files.

runCodeNew <- FALSE
#runCodeNew <- TRUE

# Ask for credentials of the Human Mortality Database if the code runs anew
if (runCodeNew){
  HMD_username <- readline(prompt = "Enter username: ")
  HMD_password <- readline(prompt="Enter password: ")
  credentials <- c(HMD_username, HMD_password)
}

# Specify filename prefix for saved files and create a folder if needed:
saveFileDir = "preprocessed_files"
if (saveFileDir %in% list.files(getwd())) {
  # Dir exists
}else{
  dir.create(file.path(".", saveFileDir), showWarnings = FALSE )
}
## NULL

1 Chapter 01 Introduction

Figure 1: Exemplary life table curves generated by Gompertz functions with different \(\beta\) parameters.

source("./chapter_01_introduction/gompertz_distribution.R")

2 Chapter 02 Materials and methods

Figure 3: Hazard curve (mx) for HMD UK data of the year 1841.

source("./chapter_02_materials_and_methods/hazard_curve.R")
## Saving 7 x 5 in image

3 Chapter 03 Data

Figure 4: Major cemeteries in Greater London 1100–1850 used in the present study.

source("./chapter_03_data/London_places.R") 
## Saving 7 x 5 in image

Table 1: Overview of included cemeteries with osteoarchaeological data.

read.table("chapter_03_data/london_cemeteries.txt", header = T, sep = "\t") %>%
  knitr::kable(., caption = "Overview of included cemeteries with osteoarchaeological data.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position") %>% unclass() %>% cat()
Overview of included cemeteries with osteoarchaeological data.
Map.nr. name period excavation.date social.character absolute.n n.analysed n….12.years references
6 Bermondsey Abbey 1089–1538 1984–1995 monks 208 201 201 Dyson et al. (2011)
8 St. Mary Spital 1120–1538 1991–2007 commoners 10,516 5,387 Connell et al. (2012)
NA period 14: 1120–1200 347 329
NA period 15: 1200–1250 510 470
NA period 16: 1250–1400 1,392 1,361
NA period 17: 1400–1539 526 467
3 St. Mary Graces 1350–1540 1986–1988 commoners 378 298 Grainger/Phillpotts (2011)
7 New Churchyard 1569–1739 2011–2015 low status 3,354 682 (category A) 556 Hartle et al. (2017)
4 St. Benet Sherehog 1670–1740 1994–1996 higher status 230 179 Miles et al. (2008a)
1 St. Marylebone 1767–1859 1992; 2003 high status 301 226 Miles et al. (2008b)
2 St. Marylebone Paddington Street north 1772–1853 2012–2013 high status 385 291 232 Henderson et al. (2015)
9 Chelsea Old church 1712–1842 2000 mixed 198 168 Cowie et al. (2008)
5 St. Brides crypt 1740–1853 high 216 Scheuer, J. L. (1995); Scheuer, L. (1998)
10 St. Brides lower churchyard 1770–1849 low 606 379 Kausmally (2008)
11 St Mary and St Michaels burial ground 1843–1854 2004–2005 low, Irish immigrants 760 705 284 Henderson et al. (2013)
12 Sheens burial ground 1763–1853 2006–2007 low 265 254 172 Henderson et al. (2013)
13 Bow Baptist church 1816–1853 2006; 2008 villagers 440 416 231 Henderson et al. (2013)

Figure 5: Population development of London, compiled from Finlay/Shearer (1986), 39 table 1; Landers (1993), 41; 179 table 5.7; Weinreb et al. (2008), 655–657.

source("./chapter_03_data/London_population.R")
grid::grid.newpage()
grid::grid.draw(rbind(london_pop1, london_pop2))

Footnote 6: Re-calculation of population increase rates of London from Razzell/Spence (2007). Calculated in ./chapter_03_data/London_population.R

knitr::kable(razz_df, caption = "Re-calculation of population increase rates of London from Razzell/Spence 2007.")%>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Re-calculation of population increase rates of London from Razzell/Spence 2007.
date population rate.per.year
1520 55000 NA
1600 200000 0.016
1650 400000 0.014
1700 575000 0.007
1750 675000 0.003
1801 960000 0.007
1851 2685000 0.021

4 Chapter 04 Results

Preprocessing of data used in figure 6: Estimated modal ages.

4.1 Historical life tables

4.1.1 Written sources

Basic statistics and Bayes (extensive) calculations

The data is referenced and aggregated in “./chapter_04_results/historical_lifetables.R”. In this file, all records from individual preprocessing files located in “./liftables_preprocessed/” are sourced. The corresponding data files are stored in “./data/”.

English_Peers.R, russell.txt, Source: La Poutré/Janssen (2021), table 2

source("./chapter_04_results/historical_lifetables.R")
kable(peers_ranges, caption = "English Peers") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English Peers
parameter modes HDI.ranges
beta 0.0613 0.0559-0.0660
M 58.1758 56.4-59.8
e20 33.4148 NA
e25 29.4926 NA

Medieval_England.R, Christ_church_monks.txt, Source: Hatcher et al. (2006), 28 table 2

kable(monks_ranges, caption = "Christ Church monks") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Christ Church monks
parameter modes HDI.ranges
beta 0.0461 0.0398-0.0523
M 52.7659 48.9-56.0
e20 31.0948 NA
e25 27.7530 NA

London_1728_1840.R, Mortality_bills_1728_1840.txt, Source: Roberts/Cox (2003), 304 Table 6.5; > 100 years and < 1 year collapsed

kable(london_1728_1840_ranges, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840.
parameter ranges
beta 0.0326-0.0418
M 43.3-54.8 
kable(london_1728_1840_ranges_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840, corrected for population growth.
parameter ranges
beta_r 0.034-0.0508
M_r 45.8-64.3
r 0.001-0.019

London_1841_raw_all.R, London_1841_raw.txt, Source: Graham (1842), 19 table q.

kable(London_1841_ranges, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Census data for London from 1841.
parameter modes HDI.ranges
beta 0.0547 0.0510-0.0585
M 60.4164 58.9-61.7

English_Mortality.R, wrigley_et_al_1997_england_1640-1809.txt, Source: Wrigley et al. (1997), 290 table 6.19

kable(eng_mort_ranges, 
      caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English mortality data.
parameter ranges
beta 0.0438-0.0608
M 52.2-67.4

HMD_UK_ranges.R

The data from the Human Mortality Database (https://mortality.org/) were retrieved with a personal account using the R package HMDHFDplus. Therefore, we only provide the processed data here.

kable(HMD_UK_ranges, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Human Mortality Database UK.
parameter ranges
beta 0.05-0.0654
M 64.2-70.2

Extended statistics

kable(peers_result, caption = "English Peers.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English Peers.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000356 1.001061 0.0044095 0.0043879 0.0043263 11315.3 0.0000044 0.95 0.0035238 0.0053575
b 1.000307 1.000854 0.0609452 0.0609518 0.0612976 11121.9 0.0000244 0.95 0.0559415 0.0660412
M 1.000196 1.000696 58.1500750 58.1648975 58.1757927 20660.4 0.0059675 0.95 56.4492001 59.8036275 
kable(monks_result, caption = "Christ Church monks.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Christ Church monks.
start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
1395 1505 alpha 1.000569 1.001661 0.0102993 0.0102563 0.0100488 13991.9 0.0000096 0.95 0.0081076 0.0125497
1395 1505 beta 1.000498 1.001436 0.0459467 0.0459287 0.0461060 13623.6 0.0000273 0.95 0.0397953 0.0523389
1395 1505 M 1.000504 1.001504 52.5281106 52.6296486 52.7658924 15808.5 0.0143226 0.95 48.9344189 55.9631681 
kable(london_1728_1840_result, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000087 1.000306 0.0146842 0.0146345 0.0145833 17556.5 0.0000101 0.95 0.0121424 0.0173529
X1728 beta 1.000115 1.000412 0.0349280 0.0349276 0.0347502 17418.0 0.0000202 0.95 0.0296810 0.0401486
X1728 M 1.000083 1.000299 44.6441200 44.8860914 45.5314756 17327.3 0.0224261 0.95 38.6469401 50.0270569
X1730 alpha 1.000130 1.000390 0.0156561 0.0155984 0.0155550 17707.3 0.0000113 0.95 0.0127651 0.0186532
X1730 beta 1.000044 1.000181 0.0325647 0.0325599 0.0325660 17242.0 0.0000212 0.95 0.0271489 0.0380817
X1730 M 1.000124 1.000377 42.2325103 42.5795321 43.3073366 17007.1 0.0285150 0.95 34.7635858 49.1029390
X1740 alpha 1.000404 1.001423 0.0153988 0.0153491 0.0151995 17959.5 0.0000100 0.95 0.0128421 0.0180871
X1740 beta 1.000376 1.001376 0.0337368 0.0337428 0.0337806 17712.7 0.0000192 0.95 0.0286838 0.0387413
X1740 M 1.000496 1.001609 43.0631632 43.3280277 43.9606200 17454.0 0.0235235 0.95 36.6700553 48.6880952
X1750 alpha 1.000135 1.000198 0.0151763 0.0151270 0.0150364 18259.1 0.0000101 0.95 0.0125377 0.0178563
X1750 beta 1.000114 1.000178 0.0342964 0.0342869 0.0341703 18177.8 0.0000196 0.95 0.0290894 0.0394288
X1750 M 1.000179 1.000275 43.5924225 43.8460270 44.4983607 17767.1 0.0230817 0.95 37.4073951 49.2703888
X1760 alpha 1.000177 1.000629 0.0145817 0.0145330 0.0143877 17316.9 0.0000100 0.95 0.0120971 0.0172323
X1760 beta 1.000136 1.000506 0.0350143 0.0350086 0.0350484 17001.2 0.0000202 0.95 0.0298241 0.0401131
X1760 M 1.000187 1.000641 44.8612069 45.0945299 45.4484334 17136.0 0.0220610 0.95 39.0545641 50.2289914
X1770 alpha 1.000210 1.000234 0.0143004 0.0142472 0.0140950 17376.2 0.0000100 0.95 0.0117447 0.0168976
X1770 beta 1.000111 1.000112 0.0356448 0.0356520 0.0357779 17075.8 0.0000206 0.95 0.0303640 0.0408917
X1770 M 1.000272 1.000317 45.4735868 45.7082853 46.2765443 17338.6 0.0215703 0.95 39.8841834 50.8485089
X1780 alpha 1.000514 1.001561 0.0136096 0.0135643 0.0135416 17117.8 0.0000093 0.95 0.0112683 0.0160201
X1780 beta 1.000465 1.001440 0.0367597 0.0367653 0.0367765 16987.0 0.0000198 0.95 0.0317257 0.0418630
X1780 M 1.000566 1.001711 46.9184820 47.1022825 47.2254317 17138.4 0.0191612 0.95 41.9217381 51.6370888
X1790 alpha 1.001017 1.003544 0.0126577 0.0126131 0.0125275 16575.3 0.0000091 0.95 0.0104144 0.0149800
X1790 beta 1.000983 1.003179 0.0385025 0.0385094 0.0386019 16305.1 0.0000206 0.95 0.0333766 0.0437012
X1790 M 1.000966 1.003389 48.8104699 48.9690668 49.1799758 17098.7 0.0174550 0.95 44.3144300 53.1380827
X1800 alpha 1.000110 1.000420 0.0116860 0.0116468 0.0115927 16299.7 0.0000084 0.95 0.0096049 0.0137829
X1800 beta 1.000087 1.000347 0.0399538 0.0399387 0.0396845 16015.0 0.0000202 0.95 0.0349411 0.0449695
X1800 M 1.000108 1.000414 50.7157959 50.8389930 51.1834695 17252.3 0.0153333 0.95 46.6384629 54.4728117
X1810 alpha 1.000243 1.000527 0.0115193 0.0114800 0.0114383 15734.5 0.0000082 0.95 0.0095164 0.0135694
X1810 beta 1.000118 1.000358 0.0383935 0.0383896 0.0384657 15460.0 0.0000197 0.95 0.0335364 0.0431518
X1810 M 1.000326 1.000622 51.2962821 51.4292427 51.6215562 16508.4 0.0161901 0.95 47.0977231 55.2320786
X1820 alpha 1.000052 1.000181 0.0104841 0.0104445 0.0102781 15011.2 0.0000079 0.95 0.0086351 0.0124260
X1820 beta 1.000027 1.000124 0.0403826 0.0403829 0.0404617 14970.0 0.0000204 0.95 0.0354909 0.0452688
X1820 M 1.000055 1.000187 53.3587767 53.4706305 53.7399168 16366.7 0.0145839 0.95 49.6763807 56.9584942
X1830 alpha 1.000258 1.000430 0.0098584 0.0098256 0.0097258 14395.4 0.0000077 0.95 0.0080812 0.0116651
X1830 beta 1.000286 1.000581 0.0420293 0.0420238 0.0418237 14224.9 0.0000211 0.95 0.0371298 0.0469784
X1830 M 1.000236 1.000371 54.4809550 54.5648372 54.7531694 16267.7 0.0133487 0.95 51.0810043 57.7147665
X1840 alpha 1.000201 1.000590 0.0103011 0.0102629 0.0101990 14208.6 0.0000081 0.95 0.0084545 0.0122232
X1840 beta 1.000209 1.000633 0.0409196 0.0409247 0.0410181 14009.2 0.0000213 0.95 0.0359043 0.0457889
X1840 M 1.000202 1.000548 53.6779375 53.7846103 53.9681394 15624.6 0.0146214 0.95 50.0085204 57.1315996 
kable(london_1728_1840_result_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840, corrected for population growth.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000216 1.000632 0.0117973 0.0117320 0.0118127 12703.3 0.0000126 0.95 0.0090855 0.0145984
X1728 beta 1.000264 1.000811 0.0383802 0.0383752 0.0385662 13742.4 0.0000251 0.95 0.0326747 0.0441749
X1728 M 1.000177 1.000534 50.6676878 50.8590788 51.5853562 13177.1 0.0252464 0.95 44.7887126 56.0258710
X1728 rate 1.000032 1.000061 0.0067646 0.0067607 0.0067957 25886.2 0.0000155 0.95 0.0018885 0.0116701
X1730 alpha 1.000059 1.000252 0.0144547 0.0143659 0.0142299 13146.7 0.0000151 0.95 0.0111507 0.0178779
X1730 beta 1.000039 1.000159 0.0340001 0.0340061 0.0339557 14387.4 0.0000246 0.95 0.0282645 0.0398947
X1730 M 1.000051 1.000222 44.9549040 45.3134221 45.8342311 13104.0 0.0348008 0.95 37.0599591 52.4002140
X1730 rate 1.000015 1.000087 0.0018961 0.0019028 0.0019156 29667.6 0.0000145 0.95 -0.0029809 0.0067911
X1740 alpha 1.000134 1.000373 0.0143016 0.0142310 0.0139908 12798.0 0.0000139 0.95 0.0113121 0.0174303
X1740 beta 1.000114 1.000346 0.0351313 0.0351306 0.0350897 13662.1 0.0000231 0.95 0.0298726 0.0404583
X1740 M 1.000145 1.000369 45.4444632 45.7017668 46.3552764 12730.5 0.0302372 0.95 38.7144365 51.8959603
X1740 rate 1.000018 1.000034 0.0016657 0.0016647 0.0013841 26006.3 0.0000154 0.95 -0.0032311 0.0064570
X1750 alpha 1.000049 1.000119 0.0124056 0.0123398 0.0121703 12999.5 0.0000128 0.95 0.0096605 0.0153459
X1750 beta 1.000114 1.000254 0.0374772 0.0374711 0.0375443 14176.6 0.0000242 0.95 0.0318783 0.0431958
X1750 M 1.000045 1.000095 49.4148732 49.6177878 50.0815627 13278.3 0.0263407 0.95 43.4814225 55.2646361
X1750 rate 1.000081 1.000287 0.0062345 0.0062421 0.0062999 26892.6 0.0000153 0.95 0.0013229 0.0111579
X1760 alpha 1.000133 1.000365 0.0116497 0.0115778 0.0113622 12538.9 0.0000123 0.95 0.0089760 0.0143165
X1760 beta 1.000123 1.000320 0.0385199 0.0385214 0.0387513 14046.2 0.0000242 0.95 0.0328950 0.0441009
X1760 M 1.000115 1.000314 50.9862854 51.1812512 51.5491083 12968.9 0.0247266 0.95 45.4054104 56.3142519
X1760 rate 1.000037 1.000142 0.0069574 0.0069683 0.0069632 25610.8 0.0000156 0.95 0.0020911 0.0118681
X1770 alpha 1.000262 1.000990 0.0119654 0.0118980 0.0118088 12468.2 0.0000127 0.95 0.0092575 0.0148053
X1770 beta 1.000151 1.000588 0.0385116 0.0384978 0.0384133 13499.5 0.0000251 0.95 0.0328164 0.0442370
X1770 M 1.000262 1.000981 50.2845848 50.4718699 50.8014826 12649.5 0.0255693 0.95 44.4684380 55.6510579
X1770 rate 1.000255 1.000978 0.0053766 0.0053775 0.0051547 26425.0 0.0000153 0.95 0.0004976 0.0102822
X1780 alpha 1.000510 1.001743 0.0099593 0.0099017 0.0097491 12281.7 0.0000108 0.95 0.0076519 0.0123387
X1780 beta 1.000584 1.001956 0.0415256 0.0415105 0.0415073 13729.8 0.0000246 0.95 0.0359297 0.0472338
X1780 M 1.000424 1.001436 54.3771628 54.5062255 54.6942083 13377.4 0.0204939 0.95 49.6650268 58.9237944
X1780 rate 1.000028 1.000137 0.0099015 0.0099020 0.0100127 24916.4 0.0000158 0.95 0.0050637 0.0148441
X1790 alpha 1.000162 1.000484 0.0075242 0.0074729 0.0073090 12760.2 0.0000085 0.95 0.0057152 0.0094630
X1790 beta 1.000225 1.000693 0.0463742 0.0463615 0.0461660 14273.5 0.0000252 0.95 0.0403834 0.0521632
X1790 M 1.000107 1.000307 59.2682552 59.3404861 59.6658408 16065.9 0.0150556 0.95 55.5022433 62.9845218
X1790 rate 1.000048 1.000143 0.0163814 0.0163799 0.0162194 25142.6 0.0000157 0.95 0.0114802 0.0212263
X1800 alpha 1.000144 1.000484 0.0066887 0.0066478 0.0066305 12151.0 0.0000078 0.95 0.0050562 0.0083976
X1800 beta 1.000078 1.000300 0.0483356 0.0483160 0.0483620 13263.3 0.0000257 0.95 0.0426266 0.0542268
X1800 M 1.000132 1.000476 60.9852657 61.0306400 60.9798946 15946.0 0.0138218 0.95 57.5412705 64.3730484
X1800 rate 1.000120 1.000381 0.0173361 0.0173323 0.0171962 22976.1 0.0000164 0.95 0.0123879 0.0221131
X1810 alpha 1.000955 1.003397 0.0061300 0.0060846 0.0059157 11868.0 0.0000074 0.95 0.0046001 0.0077324
X1810 beta 1.000895 1.003180 0.0477059 0.0476957 0.0476779 12759.7 0.0000258 0.95 0.0418983 0.0533158
X1810 M 1.000626 1.002298 63.0900868 63.1511612 63.3286616 15803.2 0.0140396 0.95 59.5468010 66.4600622
X1810 rate 1.000243 1.000880 0.0188104 0.0188125 0.0190338 21745.3 0.0000169 0.95 0.0139665 0.0237501
X1820 alpha 1.000249 1.000613 0.0055924 0.0055522 0.0054280 11381.2 0.0000069 0.95 0.0042113 0.0070737
X1820 beta 1.000239 1.000579 0.0497903 0.0497697 0.0497109 11993.8 0.0000266 0.95 0.0441232 0.0555551
X1820 M 1.000126 1.000412 63.9998648 64.0348523 64.0324397 15595.3 0.0129989 0.95 60.8212681 67.1779876
X1820 rate 1.000120 1.000469 0.0184395 0.0184350 0.0186655 21021.4 0.0000171 0.95 0.0135370 0.0232733
X1830 alpha 1.000420 1.001174 0.0055184 0.0054759 0.0054297 10602.3 0.0000072 0.95 0.0041318 0.0070030
X1830 beta 1.000315 1.000816 0.0508145 0.0508053 0.0507615 11519.5 0.0000275 0.95 0.0450319 0.0566174
X1830 M 1.000292 1.000965 63.7790204 63.8228311 63.7654406 15070.4 0.0128416 0.95 60.6337617 66.8190579
X1830 rate 1.000210 1.000768 0.0170345 0.0170393 0.0172684 20257.6 0.0000175 0.95 0.0122026 0.0219565
X1840 alpha 1.000903 1.002596 0.0054723 0.0054291 0.0053481 11006.4 0.0000070 0.95 0.0040897 0.0069422
X1840 beta 1.000552 1.001893 0.0504711 0.0504682 0.0503591 11741.2 0.0000273 0.95 0.0446290 0.0562058
X1840 M 1.000706 1.001888 64.1107439 64.1528480 64.2609238 15168.4 0.0130173 0.95 60.9779346 67.2784644
X1840 rate 1.000435 1.001221 0.0185215 0.0185225 0.0185345 20249.5 0.0000175 0.95 0.0136397 0.0234199 
kable(London_1841_result, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Census data for London from 1841.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000227 1.000481 0.0045780 0.0045654 0.0045126 15366.4 0.0000030 0.95 0.0038745 0.0053284
b 1.000173 1.000361 0.0547652 0.0547581 0.0546507 15261.7 0.0000155 0.95 0.0510256 0.0585294
M 1.000098 1.000288 60.3512664 60.3640713 60.4164328 26323.3 0.0044223 0.95 58.9378882 61.7484732 
kable(eng_mort_result, caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English mortality data.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1640 alpha 1.000116 1.000213 0.0109640 0.0109440 0.0108724 20086.8 0.0000055 0.95 0.0094508 0.0125183
X1640 beta 1.000128 1.000269 0.0473794 0.0473646 0.0471615 19457.0 0.0000160 0.95 0.0430271 0.0517521
X1640 M 1.000098 1.000168 55.8790864 55.9257645 56.0762781 22766.9 0.0074788 0.95 53.6542245 58.0607633
X1650 alpha 1.000196 1.000699 0.0086495 0.0086305 0.0086386 17477.0 0.0000050 0.95 0.0073694 0.0099516
X1650 beta 1.000238 1.000818 0.0534298 0.0534191 0.0532174 17097.8 0.0000176 0.95 0.0488730 0.0579356
X1650 M 1.000122 1.000456 59.0892102 59.1180884 59.1222939 22875.6 0.0058105 0.95 57.3707403 60.8059797
X1660 alpha 1.000538 1.001899 0.0091323 0.0091133 0.0090836 17736.5 0.0000051 0.95 0.0078190 0.0104985
X1660 beta 1.000442 1.001588 0.0507107 0.0507012 0.0506517 17263.0 0.0000172 0.95 0.0463039 0.0551739
X1660 M 1.000484 1.001711 58.8100849 58.8427992 58.8427140 22595.3 0.0063824 0.95 56.9061034 60.6611103
X1670 alpha 1.000280 1.000678 0.0109726 0.0109471 0.0109033 20090.3 0.0000056 0.95 0.0094600 0.0125515
X1670 beta 1.000338 1.000812 0.0444972 0.0445019 0.0446316 19399.7 0.0000157 0.95 0.0402542 0.0488448
X1670 M 1.000211 1.000529 56.4443366 56.5061422 56.5992418 22544.4 0.0083487 0.95 53.9239107 58.8183187
X1680 alpha 1.000560 1.001531 0.0134499 0.0134251 0.0133309 22339.5 0.0000061 0.95 0.0116869 0.0152420
X1680 beta 1.000479 1.001399 0.0435646 0.0435605 0.0437501 21337.1 0.0000151 0.95 0.0392159 0.0478531
X1680 M 1.000597 1.001611 51.9412993 52.0117614 52.1884363 23152.8 0.0091727 0.95 49.1667363 54.6014009
X1690 alpha 1.000203 1.000424 0.0100036 0.0099815 0.0099278 19068.4 0.0000053 0.95 0.0085828 0.0114492
X1690 beta 1.000217 1.000487 0.0457255 0.0457144 0.0457837 18458.1 0.0000160 0.95 0.0414631 0.0499716
X1690 M 1.000156 1.000323 58.2265512 58.2748183 58.3311613 22552.3 0.0076819 0.95 55.9044003 60.4191960
X1700 alpha 1.000247 1.000813 0.0097904 0.0097696 0.0097670 19048.9 0.0000052 0.95 0.0083976 0.0112137
X1700 beta 1.000228 1.000792 0.0469162 0.0469091 0.0468449 18524.9 0.0000160 0.95 0.0426635 0.0512282
X1700 M 1.000210 1.000697 58.3940436 58.4388608 58.4010030 22362.5 0.0073779 0.95 56.2165699 60.5292073
X1710 alpha 1.000629 1.002202 0.0076344 0.0076175 0.0075883 16583.9 0.0000046 0.95 0.0064833 0.0088178
X1710 beta 1.000810 1.002798 0.0547320 0.0547184 0.0547561 16149.3 0.0000181 0.95 0.0502213 0.0592441
X1710 M 1.000354 1.001230 61.0059909 61.0278089 61.0396872 23904.2 0.0053119 0.95 59.3643989 62.5807876
X1720 alpha 1.000438 1.001584 0.0080028 0.0079824 0.0079301 17173.5 0.0000047 0.95 0.0068173 0.0092105
X1720 beta 1.000453 1.001645 0.0560063 0.0560001 0.0558861 16622.0 0.0000179 0.95 0.0514205 0.0604697
X1720 M 1.000297 1.001094 59.7548666 59.7785061 59.8227855 23615.5 0.0051845 0.95 58.1648789 61.2877274
X1730 alpha 1.000128 1.000485 0.0067962 0.0067781 0.0067500 15125.2 0.0000045 0.95 0.0057413 0.0078882
X1730 beta 1.000132 1.000481 0.0561362 0.0561233 0.0561525 14537.5 0.0000193 0.95 0.0516431 0.0607418
X1730 M 1.000086 1.000325 62.6345173 62.6558894 62.6742840 23395.6 0.0050475 0.95 61.1122439 64.1406077
X1740 alpha 1.000185 1.000678 0.0067863 0.0067674 0.0067507 15383.6 0.0000045 0.95 0.0057019 0.0078702
X1740 beta 1.000260 1.000953 0.0566936 0.0566911 0.0568096 15043.4 0.0000191 0.95 0.0520709 0.0612724
X1740 M 1.000063 1.000245 62.4655115 62.4849711 62.4345863 22893.7 0.0051037 0.95 60.9419302 63.9688404
X1750 alpha 1.000389 1.001407 0.0053793 0.0053645 0.0053635 13451.8 0.0000040 0.95 0.0044682 0.0062959
X1750 beta 1.000443 1.001627 0.0595510 0.0595305 0.0594825 12966.5 0.0000210 0.95 0.0548610 0.0642515
X1750 M 1.000167 1.000607 65.4071998 65.4213962 65.4642394 24607.7 0.0044311 0.95 64.0354191 66.7582250
X1760 alpha 1.000180 1.000387 0.0080565 0.0080378 0.0079359 17802.8 0.0000047 0.95 0.0068516 0.0092887
X1760 beta 1.000187 1.000346 0.0488550 0.0488417 0.0488743 16840.4 0.0000169 0.95 0.0445037 0.0531121
X1760 M 1.000119 1.000328 61.9016665 61.9336352 62.0050035 23618.5 0.0063598 0.95 59.9327761 63.7618010
X1770 alpha 1.000469 1.001234 0.0067654 0.0067476 0.0066997 14881.8 0.0000045 0.95 0.0057073 0.0078687
X1770 beta 1.000501 1.001341 0.0538935 0.0538804 0.0536262 14373.8 0.0000192 0.95 0.0494452 0.0584665
X1770 M 1.000270 1.000709 63.5277738 63.5489910 63.4921572 22585.6 0.0054864 0.95 61.9173469 65.1383522
X1780 alpha 1.000347 1.001235 0.0066384 0.0066225 0.0066110 15713.1 0.0000043 0.95 0.0055976 0.0076907
X1780 beta 1.000349 1.001303 0.0570824 0.0570677 0.0571475 15127.7 0.0000188 0.95 0.0526292 0.0616896
X1780 M 1.000195 1.000710 62.7166530 62.7352113 62.7235429 24154.0 0.0048243 0.95 61.2201635 64.1540268
X1790 alpha 1.000180 1.000376 0.0058127 0.0057951 0.0057825 13899.0 0.0000042 0.95 0.0048677 0.0068164
X1790 beta 1.000229 1.000478 0.0580897 0.0580826 0.0579337 13447.1 0.0000206 0.95 0.0533856 0.0627649
X1790 M 1.000055 1.000174 64.6577738 64.6756380 64.7246120 23430.8 0.0047208 0.95 63.2361972 66.0657933
X1800 alpha 1.000697 1.002167 0.0046142 0.0045977 0.0045567 12391.5 0.0000037 0.95 0.0038253 0.0054317
X1800 beta 1.000709 1.002222 0.0608363 0.0608357 0.0608310 11940.3 0.0000219 0.95 0.0561091 0.0654678
X1800 M 1.000239 1.000822 67.4325112 67.4451148 67.4486965 26907.8 0.0039816 0.95 66.1359322 68.6958522 
kable(HMD_UK_result, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Human Mortality Database UK.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1841 alpha 1.000163 1.000417 0.0036316 0.0036148 0.0035704 13786.9 0.0000032 0.95 0.0029186 0.0043694
X1841 beta 1.000156 1.000468 0.0519888 0.0519880 0.0522191 13557.1 0.0000185 0.95 0.0476828 0.0561015
X1841 M 1.000083 1.000148 66.2542881 66.2748935 66.3111134 25227.7 0.0056085 0.95 64.4997322 67.9878895
X1845 alpha 1.000079 1.000297 0.0042938 0.0042780 0.0042669 14758.1 0.0000036 0.95 0.0034647 0.0051540
X1845 beta 1.000067 1.000247 0.0498996 0.0498859 0.0500069 14606.7 0.0000180 0.95 0.0455985 0.0541474
X1845 M 1.000065 1.000255 64.2120906 64.2353737 64.2258466 24443.1 0.0062539 0.95 62.2412879 66.0782225
X1850 alpha 1.000973 1.003549 0.0037558 0.0037391 0.0036783 13963.2 0.0000033 0.95 0.0030110 0.0045196
X1850 beta 1.000868 1.003159 0.0517607 0.0517548 0.0515669 13902.2 0.0000185 0.95 0.0475374 0.0561228
X1850 M 1.000670 1.002447 65.7445767 65.7656894 65.8470383 24788.4 0.0057544 0.95 63.9683713 67.5152044
X1855 alpha 1.000156 1.000325 0.0034310 0.0034165 0.0034148 13071.2 0.0000031 0.95 0.0027387 0.0041407
X1855 beta 1.000111 1.000252 0.0533405 0.0533264 0.0532089 12901.9 0.0000193 0.95 0.0489858 0.0575821
X1855 M 1.000055 1.000176 66.5070750 66.5214941 66.5377049 24496.9 0.0055156 0.95 64.7810996 68.1628553
X1860 alpha 1.000103 1.000169 0.0034785 0.0034615 0.0034062 13432.3 0.0000031 0.95 0.0027794 0.0041924
X1860 beta 1.000118 1.000200 0.0532621 0.0532640 0.0532106 13350.6 0.0000189 0.95 0.0490210 0.0575846
X1860 M 1.000016 1.000032 66.2956647 66.3134949 66.3500169 24949.1 0.0054798 0.95 64.5756127 67.9675086
X1865 alpha 1.000093 1.000333 0.0035991 0.0035837 0.0035330 13810.1 0.0000031 0.95 0.0028932 0.0043267
X1865 beta 1.000108 1.000353 0.0530530 0.0530491 0.0530859 13658.1 0.0000185 0.95 0.0488013 0.0572954
X1865 M 1.000045 1.000177 65.7780212 65.7953467 65.8802464 25507.4 0.0054316 0.95 64.0717897 67.4665740
X1870 alpha 1.000077 1.000191 0.0035027 0.0034908 0.0034765 13760.3 0.0000030 0.95 0.0028292 0.0042127
X1870 beta 1.000110 1.000242 0.0536849 0.0536587 0.0535650 13616.9 0.0000184 0.95 0.0495385 0.0579499
X1870 M 1.000013 1.000070 65.9071237 65.9205478 65.8577523 25746.8 0.0052524 0.95 64.2645935 67.5678728
X1875 alpha 1.000092 1.000343 0.0030605 0.0030478 0.0030211 12815.0 0.0000028 0.95 0.0024475 0.0036823
X1875 beta 1.000131 1.000471 0.0568401 0.0568279 0.0568980 12685.7 0.0000193 0.95 0.0526071 0.0611415
X1875 M 1.000031 1.000141 66.4668857 66.4785272 66.5086127 26537.0 0.0047162 0.95 64.9506366 67.9602202
X1880 alpha 1.000119 1.000291 0.0027376 0.0027242 0.0026867 12292.1 0.0000026 0.95 0.0021904 0.0033047
X1880 beta 1.000171 1.000388 0.0580794 0.0580802 0.0580583 12275.9 0.0000195 0.95 0.0538930 0.0623071
X1880 M 1.000016 1.000046 67.6639684 67.6752899 67.6594434 26763.5 0.0045057 0.95 66.2138218 69.0997903
X1885 alpha 1.000329 1.000699 0.0024297 0.0024169 0.0023954 11472.9 0.0000024 0.95 0.0019319 0.0029532
X1885 beta 1.000279 1.000617 0.0605593 0.0605577 0.0605172 11375.3 0.0000207 0.95 0.0561612 0.0648427
X1885 M 1.000124 1.000309 68.1749533 68.1842585 68.1928238 26834.9 0.0042250 0.95 66.8018933 69.5153058
X1890 alpha 1.000121 1.000451 0.0024118 0.0023997 0.0023802 11867.7 0.0000024 0.95 0.0019247 0.0029285
X1890 beta 1.000146 1.000531 0.0614665 0.0614588 0.0613662 11669.1 0.0000205 0.95 0.0571518 0.0657954
X1890 M 1.000045 1.000148 67.7519542 67.7613179 67.8037905 28081.6 0.0040695 0.95 66.4069818 69.0759956
X1895 alpha 1.000328 1.001210 0.0019825 0.0019735 0.0019634 10586.6 0.0000021 0.95 0.0015598 0.0024219
X1895 beta 1.000267 1.000994 0.0637922 0.0637712 0.0636859 10594.5 0.0000217 0.95 0.0594245 0.0681856
X1895 M 1.000224 1.000819 69.4924393 69.4994274 69.5249671 28489.7 0.0038280 0.95 68.2103261 70.7410684
X1900 alpha 1.000051 1.000194 0.0017882 0.0017794 0.0017686 10113.1 0.0000020 0.95 0.0013975 0.0021792
X1900 beta 1.000061 1.000247 0.0653147 0.0653019 0.0653664 10036.7 0.0000222 0.95 0.0609626 0.0696771
X1900 M 1.000007 1.000020 70.1656919 70.1713832 70.1615274 28126.0 0.0036879 0.95 68.9548389 71.3801825

4.2 London cemeteries

The data is mainly hard coded in the file ./chapter_04_results/Wellcome_DB.R.

Only St. Bride’s crypt is excluded but available from the Museum of London upon request. For general information: https://www.museumoflondon.org.uk go for: Collections > Archaeology at the Museum of London > Wellcome Osteological Research Database > St. Bride’s Church Fleet Street. If runCodeNew == TRUE the file ./lifetables_processing/stbrides_crypt.R will ask for the location of the retrieved dataset (Excel sheet) and process the data. In any other case pre-processed data will be loaded.

source("./lifetables_processing/stbrides_crypt.R")
source("./chapter_04_results/Wellcome_DB.R")
kable(wellcome_result, caption = "London cemeteries data.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London cemeteries data.
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.000041 1.000053 0.0120002 0.0118785 0.0116312 27017.7 0.0000115 0.95 0.0084207 0.0157789
Bermondsey Abbey 1089 1538 beta 1.000092 1.000223 0.0409482 0.0409634 0.0408251 22834.7 0.0000317 0.95 0.0316152 0.0504127
Bermondsey Abbey 1089 1538 M 1.000035 1.000044 41.8141666 42.1314316 42.5895073 29598.0 0.0208466 0.95 34.6562818 48.5270207
St. Mary Graces 1350 1540 alpha 1.000036 1.000126 0.0198007 0.0197073 0.0193784 34402.8 0.0000121 0.95 0.0155288 0.0242842
St. Mary Graces 1350 1540 beta 1.000064 1.000246 0.0346132 0.0346317 0.0348101 28166.3 0.0000249 0.95 0.0264157 0.0427714
St. Mary Graces 1350 1540 M 1.000033 1.000137 27.5831668 28.2298103 29.4924985 30498.9 0.0285239 0.95 17.5838168 36.3160347
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.000063 1.000248 0.0249305 0.0248335 0.0245704 50119.4 0.0000104 0.95 0.0204392 0.0295496
St. Mary Hospital, 1120-1200 1120 1200 beta 1.000092 1.000354 0.0363034 0.0363161 0.0362866 43635.8 0.0000180 0.95 0.0289140 0.0436573
St. Mary Hospital, 1120-1200 1120 1200 M 1.000087 1.000328 21.9080156 22.4413839 23.4629621 43383.4 0.0211197 0.95 13.0384585 29.7011243
St. Mary Hospital, 1200-1250 1200 1250 alpha 1.000043 1.000155 0.0299694 0.0298956 0.0297095 52086.8 0.0000101 0.95 0.0255000 0.0345169
St. Mary Hospital, 1200-1250 1200 1250 beta 1.000025 1.000109 0.0356600 0.0356700 0.0357998 45476.7 0.0000161 0.95 0.0288443 0.0423032
St. Mary Hospital, 1200-1250 1200 1250 M 1.000055 1.000158 16.4320472 16.9298267 18.0758477 44418.2 0.0208129 0.95 7.6947843 24.2981680
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.000091 1.000269 0.0183174 0.0182911 0.0182414 31202.6 0.0000060 0.95 0.0162463 0.0203748
St. Mary Hospital, 1250-1400 1250 1400 beta 1.000108 1.000371 0.0580880 0.0580939 0.0582603 28098.6 0.0000160 0.95 0.0527869 0.0633071
St. Mary Hospital, 1250-1400 1250 1400 M 1.000097 1.000266 31.8450682 31.8865114 31.9280610 32582.3 0.0049882 0.95 30.0500715 33.5580425
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.000002 1.000017 0.0262290 0.0261623 0.0261803 45587.4 0.0000098 0.95 0.0221812 0.0303416
St. Mary Hospital, 1400-1539 1400 1539 beta 1.000008 1.000033 0.0374915 0.0375014 0.0376554 39121.9 0.0000175 0.95 0.0307322 0.0443098
St. Mary Hospital, 1400-1539 1400 1539 M 1.000003 1.000019 21.1841557 21.5861738 22.1624360 39436.4 0.0186094 0.95 13.7960573 27.8674612
New Churchyard 1569 1739 alpha 1.000206 1.000735 0.0257462 0.0256884 0.0256373 40806.4 0.0000097 0.95 0.0219617 0.0296139
New Churchyard 1569 1739 beta 1.000199 1.000707 0.0365457 0.0365565 0.0366304 34210.3 0.0000183 0.95 0.0299048 0.0431858
New Churchyard 1569 1739 M 1.000272 1.000889 21.2258099 21.6328825 22.3306337 34934.2 0.0199246 0.95 13.7631753 27.9240717
St. Benet Sherehog 1670 1740 alpha 1.000050 1.000192 0.0159695 0.0158344 0.0155270 33614.1 0.0000129 0.95 0.0114517 0.0206629
St. Benet Sherehog 1670 1740 beta 1.000023 1.000101 0.0353051 0.0353070 0.0351919 28485.1 0.0000279 0.95 0.0260577 0.0445070
St. Benet Sherehog 1670 1740 M 1.000095 1.000224 33.9387756 34.6336624 35.6591452 31613.7 0.0300240 0.95 23.2911398 43.3188976
Chelsea Old church 1712 1842 alpha 1.000174 1.000411 0.0085200 0.0084094 0.0082628 22595.9 0.0000100 0.95 0.0056726 0.0114954
Chelsea Old church 1712 1842 beta 1.000199 1.000584 0.0413802 0.0413954 0.0417518 17223.8 0.0000397 0.95 0.0311508 0.0515880
Chelsea Old church 1712 1842 M 1.000161 1.000289 50.1444365 50.3764766 51.0339838 33034.1 0.0178106 0.95 43.6080170 56.2225789
St. Marylebone 1742 1817 alpha 1.000149 1.000345 0.0126129 0.0125100 0.0123435 30508.0 0.0000100 0.95 0.0093134 0.0161206
St. Marylebone 1742 1817 beta 1.000215 1.000442 0.0420169 0.0420316 0.0423510 24759.8 0.0000289 0.95 0.0331890 0.0510176
St. Marylebone 1742 1817 M 1.000203 1.000496 40.4873958 40.7631246 41.0720604 32601.7 0.0170323 0.95 34.2841253 46.1526087
St. Marylebone Paddington Street north 1772 1853 alpha 1.000436 1.001381 0.0099103 0.0098295 0.0097195 26865.2 0.0000088 0.95 0.0071400 0.0127678
St. Marylebone Paddington Street north 1772 1853 beta 1.000344 1.001181 0.0488440 0.0488217 0.0487464 22754.0 0.0000306 0.95 0.0397557 0.0578682
St. Marylebone Paddington Street north 1772 1853 M 1.000369 1.001168 44.6592823 44.7761855 45.0643066 35660.2 0.0118925 0.95 40.2211140 49.0258609
St. Bride’s lower churchyard 1770 1849 alpha 1.000259 1.000486 0.0062384 0.0061857 0.0061135 14003.7 0.0000074 0.95 0.0045631 0.0079738
St. Bride’s lower churchyard 1770 1849 beta 1.000420 1.000694 0.0506585 0.0506701 0.0506832 10437.9 0.0000456 0.95 0.0414962 0.0597338
St. Bride’s lower churchyard 1770 1849 M 1.000046 1.000066 53.4237068 53.4349280 53.5706223 46032.6 0.0076291 0.95 50.2007886 56.6385661
Sheen’s burial ground 1763 1854 alpha 1.000042 1.000075 0.0131427 0.0129977 0.0127000 26693.3 0.0000135 0.95 0.0089556 0.0174737
Sheen’s burial ground 1763 1854 beta 1.000055 1.000133 0.0345443 0.0345424 0.0345758 21003.0 0.0000346 0.95 0.0245852 0.0442423
Sheen’s burial ground 1763 1854 M 1.000073 1.000118 39.4407311 40.1726728 41.0201866 26097.8 0.0343739 0.95 28.5142648 49.3905589
Bow Baptist Church 1816 1854 alpha 1.000030 1.000065 0.0178398 0.0177310 0.0176005 34249.7 0.0000121 0.95 0.0135668 0.0222875
Bow Baptist Church 1816 1854 beta 1.000101 1.000176 0.0342888 0.0343015 0.0344203 27531.6 0.0000267 0.95 0.0254971 0.0428912
Bow Baptist Church 1816 1854 M 1.000127 1.000215 30.4475147 31.1788204 32.1419453 30146.9 0.0303469 0.95 19.8826484 39.5245140
St. Mary and St. Michael 1843 1853 alpha 1.000033 1.000036 0.0186259 0.0185419 0.0184065 40361.5 0.0000101 0.95 0.0147251 0.0226015
St. Mary and St. Michael 1843 1853 beta 1.000022 1.000026 0.0402565 0.0402521 0.0402023 34625.2 0.0000217 0.95 0.0323302 0.0481678
St. Mary and St. Michael 1843 1853 M 1.000054 1.000056 30.8800161 31.2177577 32.2013493 37195.7 0.0173432 0.95 24.2287121 37.0137908
St. Bride’s crypt (known age) 1740 1853 alpha 1.001301 1.004385 0.0048650 0.0048100 0.0046364 11054.4 0.0000077 0.95 0.0033513 0.0064885
St. Bride’s crypt (known age) 1740 1853 beta 1.001527 1.004999 0.0492998 0.0492831 0.0490777 10841.1 0.0000350 0.95 0.0422819 0.0564716
St. Bride’s crypt (known age) 1740 1853 M 1.000820 1.002819 59.1168993 59.1961001 59.4409448 16528.6 0.0139187 0.95 55.5069567 62.4858268
St. Bride’s crypt (estimates) 1740 1853 alpha 1.000226 1.000828 0.0054592 0.0053893 0.0052386 9799.8 0.0000103 0.95 0.0035622 0.0075345
St. Bride’s crypt (estimates) 1740 1853 beta 1.000156 1.000578 0.0421191 0.0420285 0.0422639 7187.2 0.0000633 0.95 0.0316832 0.0525833
St. Bride’s crypt (estimates) 1740 1853 M 1.000167 1.000522 60.6660579 60.6789717 60.5443274 31247.5 0.0156171 0.95 55.1575927 66.0820439 
kable(wellcome_result_r, caption = "London cemeteries data, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London cemeteries data, corrected for population growth.
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.0000838 1.0002832 0.0100400 0.0099166 0.0098446 26671.0 0.0000108 0.95 0.0067587 0.0135658
Bermondsey Abbey 1089 1538 beta 1.0000652 1.0002383 0.0433973 0.0434037 0.0433660 23814.9 0.0000314 0.95 0.0338812 0.0528532
Bermondsey Abbey 1089 1538 M 1.0000755 1.0002486 45.7191615 45.9209874 46.3252802 31878.5 0.0189265 0.95 38.9780944 52.1972837
Bermondsey Abbey 1089 1538 rate 1.0000464 1.0001265 0.0056675 0.0056664 0.0056281 103800.3 0.0000077 0.95 0.0007520 0.0104846
St. Mary Graces 1350 1540 alpha 1.0003274 1.0012227 0.0170500 0.0169374 0.0167563 32713.4 0.0000121 0.95 0.0128338 0.0213973
St. Mary Graces 1350 1540 beta 1.0003064 1.0010925 0.0371413 0.0371457 0.0369649 28970.8 0.0000250 0.95 0.0288199 0.0455081
St. Mary Graces 1350 1540 M 1.0003466 1.0012691 32.6147162 33.0717743 33.8230509 30846.2 0.0243233 0.95 23.9703547 40.3518000
St. Mary Graces 1350 1540 rate 1.0000894 1.0002944 0.0050173 0.0050061 0.0048331 101379.9 0.0000078 0.95 0.0001710 0.0099029
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.0000744 1.0001585 0.0229069 0.0228072 0.0226962 44341.4 0.0000114 0.95 0.0182959 0.0276749
St. Mary Hospital, 1120-1200 1120 1200 beta 1.0000567 1.0000892 0.0379624 0.0379679 0.0379693 42156.5 0.0000186 0.95 0.0305304 0.0455041
St. Mary Hospital, 1120-1200 1120 1200 M 1.0000605 1.0001422 24.9618796 25.3956309 26.2337065 40136.4 0.0202360 0.95 16.8345961 32.3307248
St. Mary Hospital, 1120-1200 1120 1200 rate 1.0000099 1.0000514 0.0028186 0.0028210 0.0028928 117945.2 0.0000072 0.95 -0.0019895 0.0077526
St. Mary Hospital, 1200-1250 1200 1250 alpha 0.9999993 1.0000040 0.0231033 0.0230317 0.0229400 51319.5 0.0000094 0.95 0.0190531 0.0273413
St. Mary Hospital, 1200-1250 1200 1250 beta 1.0000217 1.0000637 0.0398151 0.0398203 0.0399163 50177.3 0.0000159 0.95 0.0328604 0.0467834
St. Mary Hospital, 1200-1250 1200 1250 M 1.0000356 1.0000620 25.4303509 25.7221369 26.4088252 46593.1 0.0150515 0.95 18.9334422 31.4155340
St. Mary Hospital, 1200-1250 1200 1250 rate 1.0000017 1.0000242 0.0127656 0.0127687 0.0127411 106452.0 0.0000076 0.95 0.0079367 0.0176308
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.0001085 1.0003718 0.0162361 0.0162008 0.0161172 24263.4 0.0000075 0.95 0.0139430 0.0185303
St. Mary Hospital, 1250-1400 1250 1400 beta 1.0000542 1.0001499 0.0610252 0.0610180 0.0609588 24639.2 0.0000179 0.95 0.0556436 0.0666426
St. Mary Hospital, 1250-1400 1250 1400 M 1.0001158 1.0003940 33.6893300 33.7243315 33.8121968 26426.9 0.0061847 0.95 31.7114238 35.6535613
St. Mary Hospital, 1250-1400 1250 1400 rate 1.0000652 1.0002555 0.0048625 0.0048619 0.0048495 56023.5 0.0000104 0.95 0.0000656 0.0096677
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.0000166 1.0000616 0.0232087 0.0231347 0.0230476 40999.7 0.0000106 0.95 0.0191172 0.0274781
St. Mary Hospital, 1400-1539 1400 1539 beta 0.9999983 0.9999984 0.0399330 0.0399334 0.0400979 39068.3 0.0000179 0.95 0.0329843 0.0468700
St. Mary Hospital, 1400-1539 1400 1539 M 1.0000033 1.0000227 25.3472628 25.6468575 25.9890888 37135.2 0.0169475 0.95 18.7967809 31.3741897
St. Mary Hospital, 1400-1539 1400 1539 rate 1.0000045 1.0000266 0.0047576 0.0047563 0.0047267 101354.3 0.0000078 0.95 -0.0001426 0.0095800
New Churchyard 1569 1739 alpha 1.0000623 1.0002419 0.0214651 0.0213942 0.0213813 37857.5 0.0000101 0.95 0.0177059 0.0253639
New Churchyard 1569 1739 beta 1.0000466 1.0001393 0.0399082 0.0399066 0.0396311 34593.4 0.0000188 0.95 0.0330861 0.0467680
New Churchyard 1569 1739 M 1.0000890 1.0002876 27.3195761 27.5994740 28.1540202 34654.1 0.0165077 0.95 21.1423459 32.9791097
New Churchyard 1569 1739 rate 1.0000561 1.0002218 0.0075734 0.0075739 0.0075115 87815.4 0.0000084 0.95 0.0027115 0.0124518
St. Benet Sherehog 1670 1740 alpha 1.0005010 1.0017417 0.0134970 0.0133484 0.0131236 32108.5 0.0000125 0.95 0.0092715 0.0179378
St. Benet Sherehog 1670 1740 beta 1.0002784 1.0009850 0.0378485 0.0378673 0.0381238 29662.3 0.0000278 0.95 0.0285729 0.0473985
St. Benet Sherehog 1670 1740 M 1.0006580 1.0019397 38.9536464 39.4353572 40.0114939 32229.6 0.0258883 0.95 29.6329494 47.4271450
St. Benet Sherehog 1670 1740 rate 1.0001948 1.0007213 0.0054418 0.0054411 0.0053026 113459.8 0.0000074 0.95 0.0005932 0.0103694
Chelsea Old church 1712 1842 alpha 1.0001811 1.0006712 0.0064632 0.0063545 0.0061118 22867.0 0.0000086 0.95 0.0040611 0.0090769
Chelsea Old church 1712 1842 beta 1.0001447 1.0004428 0.0454444 0.0454725 0.0459164 18280.3 0.0000395 0.95 0.0352119 0.0560876
Chelsea Old church 1712 1842 M 1.0001534 1.0005323 55.0853288 55.1552183 55.2739107 41669.3 0.0151367 0.95 48.8997340 61.0988923
Chelsea Old church 1712 1842 rate 1.0000501 1.0001803 0.0076252 0.0076270 0.0076555 87862.5 0.0000084 0.95 0.0027145 0.0124857
St. Marylebone 1742 1817 alpha 1.0002178 1.0007255 0.0101440 0.0100444 0.0098538 29194.7 0.0000093 0.95 0.0071645 0.0133415
St. Marylebone 1742 1817 beta 1.0000874 1.0002910 0.0451501 0.0451589 0.0449632 25950.2 0.0000287 0.95 0.0360568 0.0541524
St. Marylebone 1742 1817 M 1.0002147 1.0007379 45.0635516 45.2034367 45.4143652 36064.4 0.0149196 0.95 39.3573683 50.4715628
St. Marylebone 1742 1817 rate 1.0000526 1.0002126 0.0074543 0.0074524 0.0076205 104062.2 0.0000077 0.95 0.0025216 0.0122892
St. Marylebone Paddington Street north 1772 1853 alpha 1.0002542 1.0008084 0.0067637 0.0066864 0.0065593 29077.1 0.0000067 0.95 0.0046115 0.0090270
St. Marylebone Paddington Street north 1772 1853 beta 1.0002756 1.0009405 0.0540638 0.0540510 0.0536428 26137.3 0.0000292 0.95 0.0448796 0.0633775
St. Marylebone Paddington Street north 1772 1853 M 1.0001123 1.0003558 50.5839045 50.5997478 50.6283602 49144.3 0.0098183 0.95 46.3197116 54.8777040
St. Marylebone Paddington Street north 1772 1853 rate 1.0000530 1.0002108 0.0134486 0.0134466 0.0134276 101055.9 0.0000078 0.95 0.0084954 0.0182577
St. Bride’s lower churchyard 1770 1849 alpha 1.0000541 1.0002105 0.0038968 0.0038498 0.0037027 15814.7 0.0000052 0.95 0.0026639 0.0052077
St. Bride’s lower churchyard 1770 1849 beta 1.0000695 1.0002299 0.0575269 0.0575380 0.0577583 11764.5 0.0000441 0.95 0.0481929 0.0669497
St. Bride’s lower churchyard 1770 1849 M 0.9999984 1.0000108 59.0021341 58.9401791 58.7233548 38951.3 0.0098755 0.95 55.2385781 62.9019341
St. Bride’s lower churchyard 1770 1849 rate 1.0000531 1.0002107 0.0132263 0.0132286 0.0132474 53107.5 0.0000108 0.95 0.0083422 0.0181082
Sheen’s burial ground 1763 1854 alpha 1.0000662 1.0001287 0.0084824 0.0083486 0.0082490 29144.7 0.0000098 0.95 0.0053643 0.0118347
Sheen’s burial ground 1763 1854 beta 1.0000047 1.0000219 0.0407352 0.0407525 0.0409030 24694.0 0.0000327 0.95 0.0307178 0.0508684
Sheen’s burial ground 1763 1854 M 1.0001086 1.0001918 50.5580937 50.7517380 51.2064976 37030.7 0.0206643 0.95 42.7047488 58.3109442
Sheen’s burial ground 1763 1854 rate 0.9999947 0.9999988 0.0131541 0.0131562 0.0130473 97774.3 0.0000080 0.95 0.0082386 0.0179953
Bow Baptist Church 1816 1854 alpha 1.0000692 1.0001713 0.0110446 0.0109416 0.0106667 40268.7 0.0000084 0.95 0.0078860 0.0143967
Bow Baptist Church 1816 1854 beta 1.0002517 1.0008542 0.0408050 0.0408059 0.0403874 35377.1 0.0000242 0.95 0.0317338 0.0496223
Bow Baptist Church 1816 1854 M 1.0000353 1.0000572 43.9440782 44.1432122 44.7087330 45571.5 0.0156797 0.95 37.2262949 50.3267673
Bow Baptist Church 1816 1854 rate 0.9999931 0.9999937 0.0174495 0.0174502 0.0173566 103967.3 0.0000077 0.95 0.0125694 0.0223181
St. Mary and St. Michael 1843 1853 alpha 1.0000872 1.0002508 0.0122682 0.0121878 0.0120922 46330.1 0.0000074 0.95 0.0092311 0.0154130
St. Mary and St. Michael 1843 1853 beta 1.0001028 1.0002305 0.0459884 0.0459896 0.0456965 43129.1 0.0000201 0.95 0.0377459 0.0540983
St. Mary and St. Michael 1843 1853 M 1.0000848 1.0002707 40.6968622 40.8135754 41.0106266 52560.8 0.0108411 0.95 35.7575099 45.4830250
St. Mary and St. Michael 1843 1853 rate 1.0000133 1.0000654 0.0176438 0.0176430 0.0176538 111092.8 0.0000074 0.95 0.0128035 0.0225246
St. Bride’s crypt (known age) 1740 1853 alpha 1.0004443 1.0013905 0.0032673 0.0032272 0.0031669 12848.3 0.0000049 0.95 0.0022166 0.0043711
St. Bride’s crypt (known age) 1740 1853 beta 1.0004021 1.0012201 0.0548600 0.0548491 0.0546809 12567.4 0.0000327 0.95 0.0476639 0.0620221
St. Bride’s crypt (known age) 1740 1853 M 1.0002073 1.0007301 63.6024120 63.6337709 63.7592027 32254.3 0.0081643 0.95 60.6589371 66.4269445
St. Bride’s crypt (known age) 1740 1853 rate 0.9999985 1.0000287 0.0100125 0.0100126 0.0100097 119697.3 0.0000003 0.95 0.0098169 0.0102088
St. Bride’s crypt (estimates) 1740 1853 alpha 1.0003969 1.0006972 0.0034987 0.0034246 0.0033551 9622.3 0.0000080 0.95 0.0020815 0.0050785
St. Bride’s crypt (estimates) 1740 1853 beta 1.0008229 1.0016213 0.0486144 0.0486320 0.0486948 7469.0 0.0000656 0.95 0.0373576 0.0594958
St. Bride’s crypt (estimates) 1740 1853 M 1.0000624 1.0002289 66.5428345 66.4297188 66.1209580 27068.3 0.0184177 0.95 60.6696338 72.5737015
St. Bride’s crypt (estimates) 1740 1853 rate 1.0000319 1.0000996 0.0099656 0.0099642 0.0099909 35932.4 0.0000132 0.95 0.0050923 0.0148968

5 Supplements

The chapter ‘Supporting informations’ provides details about the London cemeteries included in the study.

5.1 The Coale & Demeny life tables

Calculation of the lowest \(\beta\)-value for any of the Coale & Demeny life tables (Coale/Demeny (1983)) which is 0.0391 (the female table “West”, level 1).

source("./chapter_supplement/coale_demeny_life_tables_gompertz.R")
min(gompertz_df$Gompertz_shape)
## [1] 0.03913138

5.2 Simulations

Simulations for evaluation of algorithms for retrieving Gompertz parameters. The file “./chapter_supplement/simulations_run.R” provides various tests and plots from the evaluation process. The validity of the algorithms is tested via root mean square error (RMSE) of between expected and estimated values for Gompertz \(\beta\).

5.2.1 Known age-at-death

Figure S1: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_shapes, ncol = 3)

Figure S2: Difference between expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_diff, ncol = 3)

Table S1: Root mean square errors (RMSE) for different formulas for fitting known age-at-death, ordered ascendingly.

# table of RMSEs
kable(rmse_result[order(rmse_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Evaluation of algorithms via RMSE.
method RMSE NAs
11 Bayes (5y-cat) 0.0045054 0
10 Bayes 0.0045342 0
7 MLE 0.0047464 0
4 survival 0.0047465 0
12 Bayes (10y-cat) 0.0048206 0
8 MLE (5y-cat) 0.0048251 0
5 survival (5y-cat) 0.0048980 0
1 OLS 0.0049008 545
9 MLE (10y-cat) 0.0051441 0
2 WOLS 0.0060401 0
3 WNLS 0.0061083 14
6 survival (10y-cat) 0.0067095 0
13 Bayes poisson 0.0073576 0

Figure S3: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with estimated age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_estim_shapes, ncol = 2)

Table S2: Root mean square errors (RMSE) for different formulas for fitting estimated age-at-death, ordered ascendingly.

# table of RMSEs
kable(rmse_estim_result[order(rmse_estim_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE for estimated age-at-death.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Evaluation of algorithms via RMSE for estimated age-at-death.
method RMSE NAs
6 Bayes (cat) 0.0099026 0
8 MLE_wo_OL 0.0202114 71
1 OLS 0.0243214 442
3 WNLS 0.0293842 73
2 WOLS 0.0328083 2
5 MLE (cat) 0.0761568 0
7 Bayes poisson 0.1865772 0
4 survival (cat) 0.4731442 0

Figure S4: Detailed plot for the Bayesian model of expected Gompertz \(\beta\)-values (left) and sample size (right) vs. difference of expected/estimated Gompertz \(\beta\)-values.

#source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_bayes_diff, ncol = 2)

5.2.2 Stability of means

Show that means are stable in Bayesian modelling, regardless of the number of MCMC-steps.

source("./chapter_supplement/bayes_complete.R") # can take a few minutes
kable (bayes_complete, caption = paste0("Bayesian model with simulated dataset and different number of steps. n = ", n, ", Gompertz beta = ", round(beta, 4), ".", sep = "")) %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Bayesian model with simulated dataset and different number of steps. n = 500, Gompertz beta = 0.05.
mode thinning steps parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
known_age 1 10000 a 1.003210 1.006108 0.0028582 0.0028441 0.0027725 462.7 0.0000154 0.95 0.0022403 0.0035193
known_age 1 10000 b 1.001893 1.003920 0.0480363 0.0480265 0.0481745 488.6 0.0000947 0.95 0.0440097 0.0520917
known_age 1 10000 M 1.001259 1.003216 73.8375371 73.8501409 73.6934420 930.5 0.0357533 0.95 71.6915433 75.9608132
known_age 20 100000 a 1.000011 1.000109 0.0028495 0.0028327 0.0027934 71982.2 0.0000013 0.95 0.0022163 0.0035260
known_age 20 100000 b 1.000005 1.000090 0.0480993 0.0480962 0.0483082 71181.0 0.0000080 0.95 0.0438344 0.0521777
known_age 20 100000 M 1.000000 1.000078 73.8543153 73.8768307 73.9884330 84071.3 0.0037849 0.95 71.6339091 75.9294081
estimation 1 10000 a 1.007384 1.023678 0.0028312 0.0028026 0.0027942 167.5 0.0000382 0.95 0.0019049 0.0038193
estimation 1 10000 b 1.011691 1.038693 0.0510970 0.0508290 0.0503803 86.5 0.0005942 0.95 0.0404465 0.0624583
estimation 1 10000 M 1.005548 1.017117 71.9242579 71.9119671 72.0531786 392.2 0.1119194 0.95 67.6950056 76.3291669
estimation 20 100000 a 1.000247 1.000941 0.0027769 0.0027509 0.0027034 29177.9 0.0000026 0.95 0.0019290 0.0036726
estimation 20 100000 b 1.000354 1.001342 0.0516959 0.0514776 0.0502964 20843.0 0.0000356 0.95 0.0421542 0.0619696
estimation 20 100000 M 1.000091 1.000334 71.8362699 71.7754410 71.6155191 45976.8 0.0102799 0.95 67.6297829 76.2104655

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  1. Institute for Pre- and Proto History - Kiel University ↩︎

  2. Institute of Clinical Molecular Biology - Kiel University, ↩︎

  3. Institute for Pre- and Proto History - Kiel University, ↩︎